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The magnetic ground state and the magnetization reversal of aspherical nanoparticles are investigated by model calculations and micromagnetic simulations. Essential deviations from Kittel's domain theory occur for very flat and very elongated particles, for particles whose size is comparable to the domain-wall width, and when the particle shape is strongly nonellipsoidal. For example, the single-domain state of square rod is much less stable than that of comparable elongated ellipsoids, because most of the surface charge of long ellipsoids is located on the sides. Another specific feature of flat particles is suppression of the curling mode.